Fill in the missing statement and reason in the proof of the corresponding angles theorem.

segment ab is parallel to segment cd, and transversal ef intersects segment ab at g and segment cd at h (as seen in the photo below).

it is given that segment ab is parallel to segment cd and points e, g, h, and f are collinear. the measure of ∠egf is 180°, by the definition of a straight angle. ∠age and ∠agf are adjacent, so the measure of ∠age plus the measure of ∠agf equals the measure of ∠egf, by the angle addition postulate. then, substituting for the measure of ∠egf it can be said that the measure of ∠age plus the measure of ∠agf equals 180°. so the measure of ∠che plus the measure of ∠agf equals 180°. substituting once again means that the measure of ∠age plus the measure of ∠agf equals the measure of ∠che plus the measure of ∠agf. the measure of ∠age is equal to the measure of ∠che finally, by the definition of congruence, ∠age is congruent to ∠che.

∠che and ∠agf are alternate interior angles; using the addition property of equality

∠che and ∠agf are alternate interior angles; using the subtraction property of equality

∠che and ∠agf are same-side interior angles; using the subtraction property of equality

∠che and ∠agf are same-side interior angles; using the addition property of equality